6 Jul
2005
6 Jul
'05
5:38 p.m.
I said,
Except for the prisms and the five regular solids, even the central angles subtended by the faces are rarely nice.
Not even the prisms. The ngonal faces each subtend a solid angle of 2 %pi 2 %pi 3 %pi 2 n acos(cos (---) sqrt(sin (---) + 1) + sin (---)) n n n wrt the center, but this (half height pyramid) is only "nice" for n=4 (cube). (Although it is acos(<rational>) for n=3 and 6.) Well, OK, as n -> oo, the prism approaches a circular disk, the top and bottom of which subtend 2 pi. --rwg x